SOLUTION: The length of a rectangle is 5 cm more than 2 times its width. If the area of the rectangle is 78cm^2, find the dimensions of the rectangle to the nearest thousandth. Thanks in a

Algebra ->  Rectangles -> SOLUTION: The length of a rectangle is 5 cm more than 2 times its width. If the area of the rectangle is 78cm^2, find the dimensions of the rectangle to the nearest thousandth. Thanks in a      Log On


   

Question 60812: The length of a rectangle is 5 cm more than 2 times its width. If the area of the rectangle is 78cm^2, find the dimensions of the rectangle to the nearest thousandth.
Thanks in advance for your WONDERFUL help!
ac
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Hi ac,
The length of a rectangle is 5 cm more than 2 times its width. If the area of the rectangle is 78cm^2, find the dimensions of the rectangle to the nearest thousandth.
:
Let the width be: x
Then the length is: 2x+5
Area is: 78 cm^2
Area=length*width
:
78=x(2x+5)
78=2x^2+5x
0=2x^2+5x-78
This is in standard form:ax%5E2%2Bbx%2Bc=0
We can use the quadratic formula to solve it:highlight%28x=%28-b%2B-sqrt%28b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29%29
a=2, b=5, and c=-78
x=%28-5%2B-sqrt%285%5E2-4%282%29%28-78%29%29%29%2F%282%282%29%29
x=%28-5%2B-sqrt%2825%2B624%29%29%2F4
x=%28-5%2B-sqrt%28649%29%29%2F4
You can ignore the negative dimension.
x=5.119
The width is: x=5.119 cm
Length is:2x+5=2(5.119)+5=15.238 cm
Happy Calculating!!!